Machine learning is a specialized study on computer simulation and learning human behavior for obtaining new knowledge and skills and on reorganizing existing knowledge structure and skill to continuously improve performance. It is the core of artificial intelligence and the fundamental way of making computers intelligent. Machine learning is a multi-disciplinary subject, involving probability theory, statistics, approximation theory, convex analysis, and algorithm complexity theory. Its algorithm is widely used in many fields of engineering and science, and has advantages in terms of classification, pattern recognition, prediction, system parameter optimization, and building complex dynamic models from observations.

Ultrafast optical systems are usually complex, nonlinear, and multidimensional, and their dynamics are extremely sensitive to internal parameters and external disturbances. The design and optimization of these systems are generally based on physical models, numerical simulation, and trial and error approach. Owing to the increase in system complexity, these methods have reached their limits. Thus far, the application of machine learning in ultra-fast optics is mostly based on genetic algorithms or feedforward architecture. Although these implementations have undoubtedly brought significant results, there are still some limitations that need to be resolved . The machine learning neural network technology can find relationships among the state variables of the systems, which provides a new way to explore nonlinear dynamic systems without solving complex mathematical and physical equations. The generated nonlinear model can also be used to design and control laser characteristics. Pulse optimization in ultrafast experiments may involve multiple parameters, which are interrelated in complex ways. This is a field where neural networks can significantly surpass other forms of manual or partial automatic control. In addition, it is extremely challenging to process the data generated by ultrafast optical experiments. Traditional data processing requires to filter out the influence of noise. Solving the time-dependent Schr?dinger equation or using iterative algorithm makes the process extremely cumbersome and time-consuming. The neural network is based on the mathematics, and provides a new method combined with physical principles for efficient analysis and processing of ultrafast experimental data. Therefore, neural network has a good application prospect in the field of optics.

This review highlights the application of neural networks in ultrafast optics. Neural network plays an active role in the self-tuning and coherent dynamics control of ultrafast fiber lasers. In the processing of ultrafast optical experimental data, neural networks are applied to the study of ultrafast laser propagation dynamics, measurement of ultrafast pulse information, calculation of complex systems, and data mining involving physical laws.

Neural network has high application potential in ultrafast optical systems. On the one hand, the computing power of computer hardware is improved, which can efficiently process massive data and support more complex neural networks. On the other hand, the improvement in algorithm enables neural networks deal with more complex problems. The combination of neural networks and genetic algorithms or different types of neural networks can jointly explore the potential of machine learning and make more progress in understanding and optimizing nonlinear systems. In addition, the ability of unsupervised learning to infer and reveal hidden internal structures from datasets without labels is extremely important for noise-sensitive experimental data processing. However, there are also challenges in the application of neural networks in ultrafast optics. First, as a mathematical computing tool, neural network lacks the physical meaning. Although there have been works to integrate physical laws into the algorithms, it is still a challenge to intuitively obtain physical laws from the converged training results. Second, the training results of neural networks depend heavily on the quantity and quality of training data. However, sometimes the experimental conditions are limited and only a small amount of data can be obtained. Although training data can be obtained through theoretical simulation, the lack of noise and disturbance in the experimental environment challenges the generalization and robustness of the algorithms.

In summary, in the past few years, machine learning neural network has made significant progress in its application in ultrafast optics, and related achievements have emerged endlessly. With the progress of neural network algorithms and the development of ultrafast optics technology, we can expect that ultrafast optics study becomes more intelligent, more convenient, more automatic, and more accurate to reveal physical laws.